How to compare race times from one race to another race?

[Mike Licata]

My son competed in a race over the weekend, and we are trying to figure out how he did overall compared to kids in similar races around the country. I am not very good in math, but I want to help him. Can this/ should this be done as a percentile? How? Other thoughts about how to approach this problem? Ideally, he wants to know, what place would he have taken (or what is his percentile) if all the racers had competed in together.

He was in race #1. There were 846 racers. He finished 315 overall, and in 39th place for his age bracket (there were 88 racers in his age bracket).

In race #2, there were 1,789 racers. Considering his time, he would have finished 19th in his age bracket (there were 174 racers in his age bracket)

In race #3, there were 4,768 racers. Considering his time, he would have finished 46th in his age bracket (there were 528 racers in his age bracket).

In race #4, there were 898 racers. Considering his time, he would have finished 70th in his age bracket (there were 121 racers in his age bracket).

In race #5, there were 178 racers. Considering his time, he would have finished 23rd in his age bracket (there were 28 racers in his age bracket).

Any help/thoughts would be really appreciated!
Mike Licata
Va Beach

 

[I like Serena]

My son competed in a race over the weekend, and we are trying to figure out how he did overall compared to kids in similar races around the country. I am not very good in math, but I want to help him. Can this/ should this be done as a percentile? How? Other thoughts about how to approach this problem? Ideally, he wants to know, what place would he have taken (or what is his percentile) if all the racers had competed in together.

He was in race #1. There were 846 racers. He finished 315 overall, and in 39th place for his age bracket (there were 88 racers in his age bracket).

In race #2, there were 1,789 racers. Considering his time, he would have finished 19th in his age bracket (there were 174 racers in his age bracket)

In race #3, there were 4,768 racers. Considering his time, he would have finished 46th in his age bracket (there were 528 racers in his age bracket).

In race #4, there were 898 racers. Considering his time, he would have finished 70th in his age bracket (there were 121 racers in his age bracket).

In race #5, there were 178 racers. Considering his time, he would have finished 23rd in his age bracket (there were 28 racers in his age bracket).

Any help/thoughts would be really appreciated!
Mike Licata
Va Beach

Hi Mike Licata! Welcome to MHB!

Suppose everyone had competed in one big race.
And suppose all racers are different and only compete once (that may not actually be true though, since "good" racers may well compete more often).
Then from the first 87 racers in his age bracket, excluding your son, 38 would presumably end higher then him.
From the second 173 racers, 18 would have ended higher.
And so on.

In total 38 + 18 + 45 + 69 + 22 = 192 racers in his age bracket would have ended higher on a total of 1 + 87 + 173 + 527 + 120 + 27 = 935.
That is, he would take position 193 out of 935 positions or 193 / 935 = 20.6%.